Continuity in the Hurst parameter of the law of the Wiener integral with respect to the fractional Brownian motion

We prove the convergence in law, in the space of continuous functions C([0,T]), of the Wiener integral of a deterministic function f with respect to the fractional Brownian motion with a Hurst parameter H to the Wiener integral of f with respect to the fractional Brownian motion with a parameter H0, when H tends to H0∈(0,1/2].